Assume the current price of corn chips is $2/packet. The demand elasticity is 0.5 (ignoring the negative sign) and current consumption (quantity demanded) is 40 millions packets per week. Suppose that the manufacturer raises the price of corn chips to $4 per packet. Derive the demand equation
Demand elasticity is given as the ratio of change in quantity to change in price, or how much the demand will change if the price changes.
in simplest terms, e = (dQ/Q)/(dP/P)
Here the price changes by 100% (from $2 to $4/packet),
so, 0.5 = (dQ/Q)/100
or, dQ/Q = 50
i.e. demand will decrease by 50% as the price increases by 100%.
so, at a price of $4/packet, the demand will be 20 million packets/week.
Now, we have two data points,
(40, 2) and (20, 4)
slope of the line would be, m = (4-2)/(20-40) = -2/20 = -0.1
using the slope intercept form of equation of line, y =mx + b
we get, 2 = -0.1*40 + b
or, b = 6
thus, the demand function is: y = -0.1 x + 6
where, y is the price per packet in $ and x is the demand per week in million packets.
Hope this helps.